Uncertainty analysis of structural systems by perturbation techniques

The formulation of an efficient method to evaluate the uncertainty of the structural response by applying perturbation techniques is described. Structural random variables are defined by their mean values, standard deviations and correlations. The uncertainty of structural behaviour is evaluated by the covariance matrix of response according to the developed perturbation methodology. It is also presented the procedure used to implement this method in a structural finite element framework. The implemented computational program allows, in only one structural analysis, to evaluate the mean value and the standard deviation of the structural response, defined in terms of displacements or forces. The proposed method is exact for problems with linear design functions and normal-distributed random variables. Results remain accurate for non-linear design functions if they can be approximated by a linear combination of the basic random variables.